Questions: speeds over 200 miles per hour. Assuming a particular peregrine falcon dives at a speed of 200 miles per hour, how long will it take to reach the ground if it dives from a height of 330 feet? Hint: There are 5,280 feet in 1 mile. Write your answer as a whole number, a decimal, or a simplified fraction or mixed number. Do not round. seconds

Solution Steps

First, we need to convert the speed of the peregrine falcon from miles per hour to feet per second.

Given:

• 1 mile = 5,280 feet
• 1 hour = 3,600 seconds

The speed in feet per second is calculated as follows: \[ 200 \, \text{miles per hour} \times \frac{5,280 \, \text{feet}}{1 \, \text{mile}} \times \frac{1 \, \text{hour}}{3,600 \, \text{seconds}} \]

\[ 200 \times \frac{5,280}{3,600} = 200 \times 1.4667 = 293.3333 \, \text{feet per second} \]

Next, we need to determine how long it will take for the falcon to dive from a height of 330 feet at a speed of 293.3333 feet per second.

The time \( t \) in seconds is given by: \[ t = \frac{\text{distance}}{\text{speed}} = \frac{330 \, \text{feet}}{293.3333 \, \text{feet per second}} \]

\[ t = 1.125 \, \text{seconds} \]

Final Answer